For each of the following, fill in the blank to create a perfect-square trinomial:
(a) x2 −6x+ ____
y2 +7y+ __
recall that (a+b)^2 = a^2+2ab+b^2
so, take 1/2 of the middle coefficient and square it.
Wha't is is fill in the blaks
To determine the missing term in each perfect-square trinomial, we can follow these steps:
(a) x^2 - 6x + ____:
1. Take half of the coefficient of the middle term, which is -6 in this case: -6/2 = -3.
2. Square the result from step 1: (-3)^2 = 9.
Therefore, the missing term is 9.
Hence, the perfect-square trinomial is: x^2 - 6x + 9.
(b) y^2 + 7y + __:
1. Take half of the coefficient of the middle term, which is 7 in this case: 7/2 = 3.5.
2. Square the result from step 1: (3.5)^2 = 12.25.
Therefore, the missing term is 12.25.
Hence, the perfect-square trinomial is: y^2 + 7y + 12.25.
To create a perfect-square trinomial, we need to identify the missing terms that complete the square.
(a) For the trinomial x^2 - 6x + ____, we can find the perfect square by applying the following steps:
1. Take half of the coefficient of the x-term, which is -6 in this case.
2. Square the result obtained from the previous step.
Half of -6 is -3, and squaring -3 gives us 9. So, the missing term to create a perfect-square trinomial is 9.
Therefore, the perfect-square trinomial for (a) is:
x^2 - 6x + 9.
(b) Similarly, for the trinomial y^2 + 7y + ____, we can use the same steps:
1. Take half of the coefficient of the y-term, which is 7 in this case.
2. Square the result obtained from the previous step.
Half of 7 is 3.5, and squaring 3.5 gives us 12.25. However, since we are looking for whole numbers to complete the square, we choose a perfect square close to 12.25, which is 12.
Therefore, the perfect-square trinomial for (b) is:
y^2 + 7y + 12.